STOCKHOLM, Aug 29 (Reuters) - Swedbank has named Jens Henriksson, the head of insurer Folksam as chief executive officer, as the lender tries to rebuild confidence after a money-laundering scandal.

Sweden's oldest retail bank earlier this year dismissed its CEO, accepted the resignation of its chairman and lost more than a third of its market value after its Estonian business was caught up in money-laundering allegations that have also engulfed Danish peer Danske Bank.

Henriksson told a news conference priorities for a bank whose stock has tumbled nearly 40% this year included rebuilding its reputation and highlighting positives in its business.

"This is a crisis and a lot is about recovering our reputation," he said.

"There is a cloud of uncertainty that is hanging over Swedbank that affects the share price, the reputation of Swedbank and the people who work at Swedbank. That must be removed."

The initial reactions to the appointment announced late on Wednesday were mixed, with Credit Suisse saying it would take "leadership uncertainty off the table" while the Swedish Shareholders' Association took a dimmer view. "It is troubling that Henriksson during a long period as an owner representative had a responsibility for the development in Swedbank," association CEO Joacim Olsson told Reuters.

Folksam is the second-largest shareholder in the Swedish bank and Henriksson, with extensive experience in politics and the financial sector if less so in banking, had been widely viewed as a frontrunner for the job.

Shares in Swedbank were down 0.8% by 0758 GMT, the worst performer among Sweden's major banks, which include SEB and Handelsbanken.

In April, Swedbank admitted some failings in its money laundering processes and promised to launch a comprehensive internal investigation.

The most recent allegations against Swedbank, reported by Swedish state TV in March, say it processed gross transactions of up to 20 billion euros ($22 billion)a year from high-risk, mostly Russian non-residents through Estonia from 2010 to 2016.

CLEANING HOUSE

Swedbank is the subject of a joint investigation by the Swedish and Baltic financial watchdogs and is also being investigated in the United States.

Goran Persson, Swedbank's chairman since June, said on Thursday he had no new information about the investigations where the bank faces the threat of hefty sanctions and fines.

A Social Democrat who served as Sweden's prime minister for a decade until 2006, Persson pledged in June to "clean the house" and restore confidence in Swedbank.

He said that the bank continued to work with local and overseas authorities in addition to conducting its own investigation into the alleged money-laundering and played down Henriksson's limited banking experience.

"Many who have made mistakes during this journey, which we are trying to deal with, were very knowledgeable about regulations," he told the news conference.

"We want to come back to a situation where we can say that Swedbank is the bank that deals with these issues (money laundering) best. And we are not there now."

Henriksson repeated the bank's line ever since the money laundering scandal broke that it had no plans to exit the Baltic countries, which together with Sweden are seen as its home markets.

He will take over from acting CEO Anders Karlsson "as soon as possible", Swedbank said. He was previously CEO of the Stockholm Stock Exchange and worked at the Swedish Ministry of Finance when Persson was in government.